Yes, you definitely can back out.
One thing about the DEP some recruiters may not want you to know: In this program, you enlist, and "promise" to ship out for boot camp on the designated date. This is a binding contract, and if the military wanted to, they could prosecute you for not shipping out on the date specified on the contract. However, current regulations and policies require the military services to discharge you from the DEP, if -- at any time before shipping out -- you apply to be released from the contract (the request should be in writing and should state the reason you wish to be discharged from the DEP). If a recruiter tells you that you will go to jail if you back out of DEP, he/she's lying to you. If he/she tells you that you will never be able to enlist again, he/she is lying to you. If they tell you that you will be "blacklisted," he/she is lying to you. If he/she tells you that you will be given a "general" discharge, he/she is lying to you. In fact, the only bad consequences to dropping out of the DEP, is that if you later want to enlist in that same service, it will be on THEIR terms, not yours. Most services have policies that require a waiver processing for recruits who previously dropped out of DEP of their service. Because of this, many programs (such as guaranteed job) may not be available, should you change you mind (Note: This doesn't apply if you drop out of the DEP of one service, then join a different service).
That being said, if you request a discharge from the DEP, expect your recruiter to be (justifiably) angry. He/she's invested several hours of his/her valuable time in your enlistment, and the military has spent a significant amount of time and funds in your tests and medical physical. Additionally, if you drop out, you're no longer filling a "slot" that must be filled, and the recruiter must now try and find someone to fill that slot. Really, don't enlist in the DEP unless you are 100% sure you want to join the military.
In fact, up until you swear in again, right before you ship you can still back out with little problem. After you swear in, and ship to boot camp, it gets hairy. If you want more information on that I can provide it, but since it wasn't your question, I'll abstain for the moment.
